Realized matrix-exponential stochastic volatility with asymmetry, long memory and higher-moment spillovers

Abstract The paper develops a novel realized matrix-exponential stochastic volatility model of multivariate returns and realized covariances that incorporates asymmetry and long memory (hereafter the RMESV-ALM model), and higher-moment spillovers. The matrix exponential transformation guarantees the positive definiteness of the dynamic covariance matrix. We decompose the likelihood function of the RMESV-ALM model into two components: one based on the conventional Kalman filter, and the other evaluated by a Monte Carlo likelihood technique. We consider a two-step quasi-maximum likelihood estimator for maximizing the likelihood function, and examine the finite sample properties of the estimator. The specification enables us to analyze asymmetric and higher-moment spillover effects in the covariance dynamics via news impact curves and impulse response functions. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The forecasting performance of the new model is compared with a novel dynamic realized matrix-exponential conditional covariance model. Our empirical results suggest the RMESV-ALE specification to be superior, and spillover effects are found from returns or volatility to the remaining volatilities.